\section{Paradigm insurer} 
\label{sec:ParadigmInsurer} 

The Paradigm Insurer's future operating results depend on the variation in PI's Population Loss Ratio Estimates ($PLRE_{PI}$s), PI's standard error, $\sigma_{e_{1,000,000}}$ = $\sigma_{e_{PI}}$ = $\frac{\sigma}{\sqrt{1,000,000}}$ which I assume to be 0.0500. PI's Cumulative PLRE Distribution Function is normally distributed, $\Phi_{PI}$(0.7500, 0.0500). Insurance risk assuming health care providers are similar to insurers smaller than PI. PI's operating characteristics include:

\begin{itemize}
\item Issues 1,000,000 policies and charges each policyholder the \$4,000 ``market premium'' collecting Earned Premiums totaling \$4,000,000,000 (1,000,000 * \$4,000)
 \item Bears ``risk'' because $PLRE_{PI}$ is unknown until policies expire and accounting is complete
 \item Operating results are functions of the PLRE ($PLRE_{PI}$)
 \item Expected[Population Loss Ratio Estimate] = Population Loss Ratio (0.7500)
 \item Incurs ``Underwriting Expenses\index{Underwriting Expenses}'' of \$0.15 per premium dollar (\$600,000,000)
 \item Charges policyholders a market based ``Profit Margin''\index{Profit margin} of 5\% (\$200,000,000)
 \item Charges policyholders a market based ``Risk Premium\index{Risk Premium}'' of 5\% (\$200,000,000)
 \item Pays Claims Costs of \$3,000,000,000 or less ($PLRE_{PI}$ $\leq$ 0.7500) from current revenues, earning profits of at least 10\%, with probability 0.5000
 \item Pays Claims Costs of \$3,200,000,000 or less ($PLRE_{PI}$ $\leq$ 0.8000) from current revenues, earning profits of at least 5\%, with probability 0.8413
 \item Pays Claims Costs of \$3,400,000,000 or less ($PLRE_{PI}$ $\leq$ 0.8500) from current revenues, and avoids net operating losses, with probability 0.9772
 \item Starts the year with Surplus\index{Surplus} of \$200,000,000 protecting itself from Claims Costs up to \$3,600,000,000 ($PLRE_{PI} \leq 0.9000$)
 \item Becomes insolvent (Probability = 0.00135) when Claims Costs $>$ \$3,600,000,000
\end{itemize}

Table~\ref{tab:InsurerOperatingResultsByPortfolioSize} Column 4, highlights PI's future operating results. Before proceeding, I stress that all insurers, and all health care providers, operate as efficiently as possible. I will show that small insurers and small, clinically efficient, capitated health care providers must cut services below the level PI provides. Capitation cannot create more efficient health care (finance) systems because it cannot work in efficient health care (finance) systems. 

